This paper looks at one area of potential crosslinguistic variation in comparatives. It has recently been claimed that Japanese clausal comparatives lack degree abstraction structures in the complement of yori ‘than’. Based on data from several empirical domains such as predicative adjectival comparatives, intensional contexts, and negative islands, this paper shows that Japanese clausal comparatives do not in general contrast with their English counterparts in the way predicted by the above claim. The syntactic and semantic phenomena observed in (...) Japanese clausal comparatives receive straightforward accounts if we assume that they do involve degree abstraction and degree comparison, along the lines familiar from analyses of their English counterparts. (shrink)

In this paper we document the developmental trajectory of the complementizer system (CP-system) in Italian by looking at the earliest spontaneous production of eleven young children, whose transcriptions are available on CHILDES. We conducted a novel corpus analysis, tracking down a number of constructions in which the clausal left-periphery is activated. First, we considered the appearance of the different complementizer particles in the CP-system, which overtly realize the three distinct functional projections ForceP, IntP, and FinP. The analysis revealed that (...) children acquiring Italian correctly use these complementizer particles already in the third year of life. Second, we looked for the simultaneous activation of different functional projections within the CP-system. We went through our corpus searching for complex sentences in which more than one constituent was moved to the left periphery. This option is allowed by the adult grammar of Italian and, as our search revealed, it is also attested in the grammar of young children. Soon after their second birthday, sequences in which a left-dislocated Topic and a Wh- element co-occur are attested, directly supporting the existence of a (high) Topic position above FocusP. Moreover, movement in general conforms to the constraints of the adult grammar, with no attested violation of obligatory inversion (a consequence of the Q-Criterion). Importantly, “why-questions” did not require inversion, much as in the adult grammar of Italian. Taken together, children's use of complementizer particles and their activation of multiple landing sites for movement show that 2-year-olds already possess a richly articulated functional structure of the CP-system, aligned to the layered adult structure. In concluding the paper, we also discuss some temporal differences between constructions activating high and low portions of the CP-system. In particular, we detect a temporal precedence for wh-questions over why-questions. Since the former activate a lower projection, this is consistent with the recently proposedGrowing Treeshypothesis, according to which the development of the CP-system proceeds stepwise. (shrink)

Clausal complements of different kinds of attitude verbs such as believe, doubt, be surprised, wonder, say, and whisper behave differently semantically in a number of respects. For example, they differ in the inference patterns they display. This paper develops a semantic account of clausal complements using partial logic which accounts for such semantic differences on the basis of a uniform meaning of clauses. It focuses on explaining the heterogeneous inference patterns associated with different kinds of attitude (...) verbs, but it contributes also to explaining differences among clausal complements of attitude verbs regarding the possibility of de re reference, anaphora support, presupposition satisfaction, and the distribution of subjunctive in certain languages. Moreover, it gives a new account of factivity. The point of departure of this paper is the general observation that the failure of inferences from attitude reports is relative in that it depends both on the general type of attitude and on the particular instance of the attitude described. Thus, from John is surprised that P and Q one cannot infer John is surprised that P and John is surprised that Q, though this is possible with believe. Conversely, one can infer from John believes that P and John believes that Q, to John believes that P and Q, but only as long as the same belief state of John is involved. In order to capture this dependency of inferences from attitude reports on a particular mental state or act, I propose an account on which clausal complements of attitude verbs (as well as independent sentences) characterize the intentional state or act described by the attitude verb in question, rather than referring to independent propositions. The semantic account of attitude reports of this paper can hence be called an 'event-based account' of clauses. Formally, the denotation of any sentence, both independent and embedded, is construed as a function mapping an intentional state or act to a function from situations (which form the content of the state or act) to truth values.. (shrink)

Current textbooks in formal semantics are all versions of, or introductions to, the same paradigm in semantic theory: Montague Grammar. Knowledge of Meaning is based on different assumptions and a different history. It provides the only introduction to truth- theoretic semantics for natural languages, fully integrating semantic theory into the modern Chomskyan program in linguistic theory and connecting linguistic semantics to research elsewhere in cognitive psychology and philosophy. As such, it better fits into a modern graduate or undergraduate program in (...) linguistics, cognitive science, or philosophy. Furthermore, since the technical tools it employs are much simpler to teach and to master, Knowledge of Meaning can be taught by someone who is not primarily a semanticist. Linguistic semantics cannot be studied as a stand-alone subject but only as part of cognitive psychology, the authors assert. It is the study of a particular human cognitive competence governing the meanings of words and phrases. Larson and Segal argue that speakers have unconscious knowledge of the semantic rules of their language, and they present concrete, empirically motivated proposals about a formal theory of this competence based on the work of Alfred Tarski and Donald Davidson. The theory is extended to a wide range of constructions occurring in natural language, including predicates, proper nouns, pronouns and demonstratives, quantifiers, definite descriptions, anaphoric expressions, clausal complements, and adverbs. Knowledge of Meaning gives equal weight to philosophical, empirical, and formal discussions. It addresses not only the empirical issues of linguistic semantics but also its fundamental conceptual questions, including the relation of truth to meaning and the methodology of semantic theorizing. Numerous exercises are included in the book. (shrink)

The standard view of "believes" and other propositional attitude verbs is that such verbs express relations between agents and propositions. A sentence of the form “S believes that p” is true just in case S stands in the belief-relation to the proposition that p; this proposition is the referent of the complement clause "that p." On this view, we would expect the clausal complements of propositional attitude verbs to be freely intersubstitutable with their corresponding proposition descriptions—e.g., "the proposition (...) that p"—as they are in the case of "believes." In many cases, however, intersubstitution of that-clauses and proposition descriptions fails to preserve truth value or even grammaticality. These substitution failures lead some philosophers to reject the standard view of propositional attitude reports. Others conclude that propositional attitude verbs are systematically ambiguous. I reject both these views. On my view, the that-clause complements of propositional attitude verbs denote propositions, but proposition descriptions do not. (shrink)

This book collects nine seminal essays by Mark Richard published between 1980 and 2014, alongside four new essays and an introduction that puts the essays in context. Each essay is an attempt, in one way or another, to understand the idea of a proposition. Part I discusses whether the objects of thought and assertion can change truth value over time. Part II develops and defends a relativist view of the objects of assertion and thought; it includes discussions of the nature (...) of disagreement, moral relativism, and responds to important objections to relativism. It also explores the idea that thoughts and assertions may be neither true nor false. Part III discusses issues having to do with relations between sentential and propositional structure. Among the topics discussed in Part III are the semantics of quotation, 'mixed quotation', opacity, philosophical analysis and propositional structure, and the semantics of demonstratives and clausal complements. (shrink)

Sententialism is the view that intensional positions in natural languages occur within clausal complements only. According to proponents of this view, intensional transitive verbs such as 'want', 'seek' or 'resemble' are actually propositional attitude verbs in disguise. I argue that 'conceive' cannot fit this mould: conceiving-of is not reducible to conceiving-that. I offer a new diagnosis of where Berkeley's 'master argument' goes astray, analysing what is odd about saying that Hylas conceives a tree which is not conceived. A (...) sententialist semantics cannot account for the absurdity in attitude ascriptions of this type: we need to acknowledge irreducibly non-propositional conceiving. (shrink)

The pragmatic framework developed by H.P. Grice in “Logic and Conversation” explains how a speaker can mean something more than, or different from, the conventional meaning of the sentence she utters. But it has been argued that the framework cannot give a similar explanation for cases where these pragmatic effects impact the understood content of an embedded clause, such as the antecedent of a conditional, a clausal disjunct, or the clausal complement of a verb. In this paper, I (...) show that such an explanation is available. One of the central arguments of the paper is that in a significant subset of cases, local pragmatic effects are a consequence of a global pragmatic requirement. In these cases, local pragmatic effects are a consequence of ‘acting locally’ to resolve a potential global pragmatic violation. These cases do not require us to posit application of pragmatic principles to the contents of embedded clauses. The account does, though, require the assumption that interpreters can identify and reason about the contents of unasserted sub-parts of sentences, an assumption that I motivate in section 3. Building on this, in section 4 of the paper, I argue that once we have recognized that interpreters can, and do, reason independently about the contents of non-asserted clauses, it becomes unproblematic to assume that in some cases, Gricean conversational principles do apply directly to these contents, providing an alternative route to account for local pragmatic effects. In revisiting the ideas of this paper in my response to the commentaries, I consider in more detail the revisions to Grice’s broader program that are necessitated by these moves, in particular acknowledging the problematicity of Grice’s notion of what is said. I argue that the starting point for Gricean reconstructions should instead be merely what is expressed, which carries no pragmatic commitments regarding what is speaker meant. (shrink)

Propositions have played a central role in philosophy of language since Frege. I will argue that the notion of a proposition, because of a range of philosophical problems as well as problems of linguistic adequacy, should be replaced by a different notion, for almost all the roles for it has been invoked, namely by the notion of an attitudinal object. Attitudinal objects are entities like ‘John’s belief that S’, ‘John’s claim that S’, and ‘John’s desire to do X’. Attitudinal objects (...) are closely related to, yet ontologically distinct from mental events and speech acts. (shrink)

This paper presents novel data regarding the logophoric pronoun in Ewe. We show that, contrary to what had been assumed in the absence of the necessary fieldwork, Ewe logophors are not obligatorily interpreted de se. We discuss the prima facie rather surprising nature of this discovery given the assumptions that de se construals arise via binding of the pronoun by an abstraction operator in the left periphery of the clausal complement of an attitude predicate, and that logophors are elements (...) that are obligatorily bound by such abstractors. We show that this approach can be reconciled with these facts given the additional assumption that elements that are ‘de se’ bound can interact with the concept generator variables posited by Percus and Sauerland to derive de re interpretations of embedded nominals. The proposed set-up has consequences for our understanding of puzzles raised by Heim and Sharvit concerning binding-theoretic effects with de re elements, and for the derivation of the obligatorily de se interpretation of controlled PRO. (shrink)

A formal semantic analysis of the _tough_-construction is provided building on the well-known observation that _events_ play a central role. A close look at the semantic characteristics of the class of _tough_-predicates and the syntactic and semantic properties of nonfinite clauses reveals the link between these pieces, expanding on recent advances in the semantics of clauses (Moulton in Natural selection and the syntax of clausal complementation, PhD thesis, University of Massachusetts at Amherst, 2009 ). Building on Salzmann (Reconstruction and (...) resumption in indirect A′-dependencies: On the syntax of prolepsis and relativization in (Swiss) German and beyond, de Gruyter, Berlin 2017b ), a formal semantic and syntactic analysis of prolepsis is provided to explain the antecedent gap chain in the _tough_-construction. In total, this paper offers a description and explanation of (i) the class of _tough_-predicates; (ii) the properties of the nonfinite clause that appears in the _tough_-construction; (iii) why no other predicates or clauses are permitted in the construction; (iv) the many properties of the antecedent gap chain in the _tough_-construction, primarily the fact that the chain is “weakly” unbounded; and (v) the semantic contribution of prolepsis as it applies in the _tough_-construction. (shrink)

This volume presents studies on pronouns in embedded contexts, and offers fundamental insights into this central area of research. Much of the recent research on pronouns has shown that embedded environments, such as clausal complements of attitude predicates, provide a window into the nature of pronouns. Pronouns in such environments not only exhibit familiar distinctions such as that between bound and referential pronouns; if they refer to the attitude holder, they also participate in a broader range of phenomena, (...) e.g., distinguishing between a de se reading and a de re reading. Topics covered include: the semantics of attitude reports that contain pronominal elements, the semantics of pronominal features and their connection to indexicality, new insights in the connection of pronominal typology and logophoricity or anti-logophoricity, and finally, the localization of embedded pronouns within a bigger picture involving the nature of perspective and the analysis of quasi-pronominal phenomena such as sequence of tense. (shrink)

Prior’s problem consists in the impossibility of replacing clausal complements of most attitude verbs by ‘ordinary’ NPs; only ‘special quantifiers’ that is, quantifiers like 'something' permit a replacement, preserving grammaticality or the same reading of the verb: (1) a. John claims that he won. b. ??? John claims a proposition / some thing. c. John claims something. In my 2013 book Abstract Objects and the Semantics of Natural Language, I have shown how this generalizes to nonreferential complements (...) of various other intensional predicates and argued for a Nominalization Theory of special quantifiers. In this paper, I will review and extend the range of linguistic generalizations that motivate the Nominalization Theory and show that they pose serious problems for higher-order and substitutional analyses of special quantifiers. (shrink)

This paper presents a systematic semantic study of constructions with the noun 'case'. It argues that 'cases' are situations acting as truthmakers within a sentential or epistemic case space. It develops a truthmaker-based alternative semantics of 'case'-constructions, based on Fine's recent truthmaker semantics.

Recent work on mood choice considers fine-grained semantic differences among desire predicates (notably, ‘want’ and ‘hope’) and their consequences for the distribution of indicative and subjunctive complement clauses. In that vein, this paper takes a close look at ‘intend’. I show that cross-linguistically, ‘intend’ accepts nonfinite and subjunctive complements and rejects indicative complements. This fact poses difficulties for recent approaches to mood choice. Toward a solution, a broad aim of this paper is to argue that—while ‘intend’ is loosely (...) in the family of desire predicates—it differs from ‘want’ and ‘hope’ in that it has a causative component, and this is relevant to its mood choice behavior, given that causative predicates also systematically reject indicative complements. More concretely, my analysis has three ingredients: (i) following related proposals in philosophy, intention reports have causally self-referential content; (ii) encoding causal self-reference requires abstraction over the complement clause’s eventuality argument; and (iii) nonfinite and subjunctive clauses enable such abstraction but indicative clauses do not. Aside from causative predicates, independent support for the proposal comes from the syntax of belief-/intention-hybrid attitude predicates like ‘decide’ and ‘convince’, anankastic conditional antecedents, aspectual predicates, and memory and perception reports. Synthesizing this result with that of previous literature, the emergent generalization is that subjunctive mood occurs in attitude reports that involve either comparison or eventuality abstraction. Toward a unified theory of mood choice, I suggest that both comparison and eventuality abstraction represent departures from the clausal semantics of unembedded assertions and consequently that subjunctive mood signals such a departure. (shrink)

In this essay I will explore the syntactic expression of the notion ‘clause’ by focusing on some syntactic and semantic properties of bare infinitive (BI) complements to perception verbs in English. I shall argue briefly that perception BI complements must be clausal, and then turn in more detail to the issue of what sort of clause the BI complement must be. It will be established that the categorical nature of the perception BI complement as IP or VP (...) is contingent on selectional properties of the perception verb, properties which may be contextually influenced by modality and negation. More specifically, an interpretative distinction between ‘vision’ and ‘non-vision’see first suggested by Napoli (1988) will be shown, contrary to her proposal, to provide the key to the contrast in the selection of clausal types. The IP/VP distinction will be shown to correlate with the viability of interpretations for the BI clause that are ‘temporally independent’ of the matrix clause. Given the IP/VP distinction, it will be demonstrated further that the peculiarly limited distribution of the expletive formativethere in BI complements may be predicted from independently motivated syntactic principles that determine clausal structure. (shrink)

The study considers development and use of verb/predicate chaining constructions by Hebrew speakers from early childhood to adolescence, based on analysis of authentic conversational and narrative corpora. Three types of such constructions are considered, ordered hierarchically by stage of acquisition: (1) monoclausal extended predicates consisting of a verb (modal, aspectual, or evaluative) marked for tense or mood and followed by one or more complements in the infinitive – e.g., yaxol la-asot ‘can, is able to-do’; (2) coreferential interclausal predicate chaining; (...) and (3) mature discursively-motivated topic-chaining. Relevant typological features of Modern Hebrew are reviewed to explain the lack of canonic clause-chaining construction in the language (e.g. the paucity of non-finite constructions in everyday usage, lack of an uninflected basic form of verbs, lack of auxiliary verbs expressing categories of aspect and voice, and monolexemic verb-internal complexity). Monoclausal verb-chaining emerges early in the speech of toddlers in interaction with their caretakers, whereas predicate chaining by coordination across clauses occurs only later, and chunking of such constructions at the service of discourse connectivity is a late-developing device. Nonfinite subordination is an advanced form of clause-combining, in contrast to straightforward subordination with the multifunctional subordinator še’that’. The conclusion is that, unlike the obligatorily fused monoclausal “extended predicates”, bi- and multi-clausal predicate chaining represents an optional rhetorical choice on the part of a given speaker-writer in a particular communicative context. (shrink)

Speakers often answer a question with what appears to be merely a phrase, a fragment of a sentence, rather than with a full sentence. Merchant (2004) offers an analysis of fragment answers in which the new information/answer is fronted to a clause-peripheral position and the remainder of the sentence is not pronounced. Two written acceptability judgment experiments are reported that tested predictions of this analysis. The first, in English, tested the prediction that clausal fragment answers should only be fully (...) acceptable when the clausal answer is introduced by an overt complementizer (What did May deny? That Josh left.). This is because clauses may front only when an overt complementizer is present (That Josh left, May denied, but not *Josh left, May denied). The second study was conducted in German, a language that does not permit prepositions to be stranded, left behind, when a noun phrase is moved in overt syntactic structures such as questions or topicalizations. Consequently, when the object of a preposition is questioned, only a prepositional phrase fragment answer, not a noun phrase fragment answer, is predicted to be fully acceptable. Both predictions were confirmed. The results support the claim that syntactic structure is present in unpronounced constituents, and tells against theories of syntax that eschew such structures. (shrink)

This is a study of the syntax and semantics of reports containing speech-act and propositional attitude verbs with quotational complements. I make the case that while the quotational complements of some verbs, including _utter_, are nominal and metalinguistic, those of others, including _assert_ and _believe_, are clausal and nonmetalinguistic. Quotational reports with ‘say’ are ambiguous. When quotational complements are clausal, they are like _that_-clauses in being subordinate content clauses with main-clause form. Unlike _that_-clauses, quote-clauses force (...) deictic shift and are unambiguously opaque. I also argue that quotation marks serve a different function in “mixed” reports, and that use of the traditional “direct” and “indirect” is not consistent with their traditional definitions. (shrink)

In Attitude Problems, I gave an account of opacity in the complement of intensional transitive verbs that combined neo-Davidsonian event-semantics with a hidden-indexical account of substitution failure. In this paper, I extend the account to clausal verbs.

This unique book provides a gentle introduction to an increasingly important type of formal logic called CLAUSAL FORM LOGIC (CFL). Having evolved out of human reasoning, CFL represents the ideal to which all computer-based systems must approximate. Most present day computational logic systems are based on it, including the well-know artificial intelligence language PROLOG.

In Basque, wh-movement can pied-pipe an entire clause. The surface syntax of clausal pied-piping structures suggests that their syntax and semantics should be similar to scope marking constructions as analyzed in the Indirect Dependency approach. However, data having to do with presupposition projection and the interpretation of how many-questions show that clausal pied-piping structures are actually more similar to their long-distance wh-movement counterparts than to scope marking constructions. I develop an analysis which takes into account these facts. Specifically, (...) I show that pied-piped clauses must reconstruct, which makes the correct prediction that clausal pied-piping, unlike long-distance wh-movement, is sensitive to negative islands. Finally, I propose that reconstruction is forced by a condition on the interpretation of traces. (shrink)

Clausal edges seem to have an effect on the scopes that arguments residing at those edges can have. In particular, they influence whether an argument may be interpreted at a lowered, or reconstructed, position within the clause. This is probably what is responsible for the difference between (1a) and (1b), which formed the focus for the debate in Stowell 1991 and Williams..

"The idea for this book arose in connection with the Workshop on Semantic functions of complementizers in European languages, which we organized in October 28-29, 2011, at the University of Copenhagen, Denmark. Around two thirds of the book chapters are elaborations on contributions to this workshop, the remaining one third arose independently of the workshop.".

A clausal logic allowing to handle term-graphs is defined. Term-graphs are a generalization of terms (in the usual sense) possibly containing shared subterms and cycles. The satisfiability problem for this logic is shown to be undecidable (not even semi-decidable), but some fragments are identified for which it is semi-decidable. A complete (w.r.t validity) calculus for these fragments is proposed. Some simple examples give a taste of this calculus at work.

A finer-grained delineation of a given explanandum reveals a nexus of closely related causal and non- causal explanations, complementing one another in ways that yield further explanatory traction on the phenomenon in question. By taking a narrower construal of what counts as a causal explanation, a new class of distinctively mathematical explanations pops into focus; Lange’s characterization of distinctively mathematical explanations can be extended to cover these. This new class of distinctively mathematical explanations is illustrated with the Lotka-Volterra equations. There (...) are at least two distinct ways those equations might hold of a system, one of which yields straightforwardly causal explanations, but the other of which yields explanations that are distinctively mathematical in terms of nomological strength. In the first, one first picks out a system or class of systems, finds that the equations hold in a causal -explanatory way; in the second, one starts with the equations and explanations that must apply to any system of which the equations hold, and only then turns to the world to see of what, if any, systems it does in fact hold. Using this new way in which a model might hold of a system, I highlight four specific avenues by which causal and non- causal explanations can complement one another. (shrink)

A finer-grained delineation of a given explanandum reveals a nexus of closely related causal and non-causal explanations, complementing one another in ways that yield further explanatory traction on the phenomenon in question. By taking a narrower construal of what counts as a causal explanation, a new class of distinctively mathematical explanations pops into focus; Lange’s characterization of distinctively mathematical explanations can be extended to cover these. This new class of distinctively mathematical explanations is illustrated with the Lotka–Volterra equations. There are (...) at least two distinct ways those equations might hold of a system, one of which yields straightforwardly causal explanations, and another that yields explanations that are distinctively mathematical in terms of nomological strength. In the first case, one first picks out a system or class of systems, and finds that the equations hold in a causal–explanatory way. In the second case, one starts with the equations and explanations that must apply to any system of which the equations hold, and only then turns to the world to see of what, if any, systems it does in fact hold. Using this new way in which a model might hold of a system, I highlight four specific avenues by which causal and non-causal explanations can complement one another. _1_. Introduction _2._ Delineating the Boundaries of Causal Explanation _2.1._ Why construe causal explanation narrowly? The land of explanation versus grain-focusing _2.2._ Reasons to narrow the scope of causal explanation _3._ Broadening the Scope of Mathematical Explanation _4._ Lotka–Volterra: Same Model, Different Explanation Types _4.1._ General biocide in the Lotka–Volterra model _4.2._ Two ways a model can hold, yielding causal versus mathematical explanations _5._ Four Complementary Relationships between Mathematical and Causal Explanation _5.1._ Slight reformulations of explananda _5.2._ Causal distortion of idealized mathematical models _5.3._ Partial explanations requiring supplementation _5.4._ Explanatory dimensionality _6._ Conclusion. (shrink)

A key factor that affects whether and at what age children can demonstrate an understanding of false belief and complement‐clause constructions is the type of task used (whether it is implicit/indirect or explicit/direct). In the current study, we investigate, in an implicit/indirect way, whether children understand that a story character's belief can be true or false, and whether this understanding affects children's choice of linguistic structure to describe the character's belief or to explain the character's belief‐based action. We also measured (...) children's understanding of false belief in explicit false‐belief tasks. English‐ and German‐speaking young 4‐ and 5‐year‐olds as well as English‐ and German‐speaking adult controls heard complement‐clause constructions in a story context where the belief mentioned in the complement clause (e.g., “He thinks thatshe's not feeling well”) turned out to be false, true, or was left open. After hearing the test question (“Why does he not play with her?”), all age groups were most likely to repeat the whole complement‐clause construction when the belief turned out to be false. That is, they tended to explicitly refer to the character's perspective and say “He thinks…” When the belief turned out to be true, participants often reverted to a simple clause (“She's not feeling well”). Furthermore, children with better short‐term memory were more likely to repeat the whole complement‐clause construction. However, children's performance in explicit false‐belief tasks showed no relation to their performance in our novel, more implicit/indirect, task. Whether or not the complement clause was introduced by athatcomplementizer only had a small effect on the German adults’ responses, where leaving out the complementizer also changes the word order of the complement clause. Overall, our results suggest that task characteristics and individual differences in short‐term memory affect children's ability to demonstrate false‐belief understanding and to express this understanding linguistically. (shrink)

It is well known that in Bishop-style constructive mathematics, the closure of the union of two subsets of ℝ is ‘not’ the union of their closures. The dual situation, involving the complement of the closure of the union, is investigated constructively, using completeness of the ambient space in order to avoid any application of Markov's Principle.

In this paper, I address the problem wherein the same English word permits one of its complement positions to be satisfied by phrases of different categories. A well-known example of such an English word is the copula to be, whose complements include adjective phrases, noun phrases, prepositional phrases and adverbial phrases. I provide a way to treat such words, in particular verbs, as single lexical items through a conservative extension of the usual treatment of word classification as a pair (...) comprising a part of speech category and a complement list. I then show how a further conservative extension of complement lists permits a satisfactory formalization of doubly complemented English verbs which are synonymous under a permutation of their complements. These verbs include, but are not limited to, so-called double object constructions. (shrink)

Say that a nonzero c. e. degree b is a quasi-complement of a c. e. degree a if a ∩ b = 0 and a ∪ b is high. It is well-known that each cappable degree has a high quasi-complement. However, by the existence of the almost deep degrees, there are nonzero cappable degrees having no low quasi-complements. In this paper, we prove that any nonzero cappable degree has a low2 quasi-complement.

We examine, from a constructive perspective, the relation between the complements of S, T, and S ∩ T in X, where X is either a metric space or a normed linear space. The fundamental question addressed is: If x is distinct from each element of S ∩ T, if s ϵ S, and if t ϵ T, is x distinct from s or from t? Although the classical answer to this question is trivially affirmative, constructive answers involve Markov's principle (...) and the completeness of metric spaces. (shrink)

Mortensen studies dual intuitionistic logic by dualizing topos internal logic, but he did not study a sequent calculus. In this paper I present a sequent calculus for complement-topos logic, which throws some light on the problem of giving a dualization for LJ.

Two algebraic structures, the contrapositionally complemented Heyting algebra (ccHa) and the contrapositionally |$\vee $| complemented Heyting algebra (c|$\vee $|cHa), are studied. The salient feature of these algebras is that there are two negations, one intuitionistic and another minimal in nature, along with a condition connecting the two operators. Properties of these algebras are discussed, examples are given and comparisons are made with relevant algebras. Intuitionistic Logic with Minimal Negation (ILM) corresponding to ccHas and its extension |${\textrm {ILM}}$|-|${\vee }$| for c|$\vee (...) $|cHas are then investigated. Besides its relations with intuitionistic and minimal logics, ILM is observed to be related to Peirce’s logic and Vakarelov’s logic MIN. With a focus on properties of the two negations, relational semantics for ILM and |${\textrm {ILM}}$|-|${\vee }$| are obtained with respect to four classes of frames, and inter-translations between the classes preserving truth and validity are provided. ILM and |${\textrm {ILM}}$|-|${\vee }$| are shown to have the finite model property with respect to these classes of frames and proved to be decidable. Extracting features of the two negations in the algebras, a further investigation is made, following logical studies of negations that define the operators independently of the binary operator of implication. Using Dunn’s logical framework for the purpose, two logics |$K_{im}$| and |$K_{im-{\vee }}$| are discussed, where the language does not include implication. The |$K_{im}$|-algebras are reducts of ccHas and are different from relevant algebraic structures having two negations. The negations in the |$K_{im}$|-algebras and |$K_{im-{\vee }}$|-algebras are shown to occupy distinct positions in an enhanced form of Dunn’s kite of negations. Relational semantics for |$K_{im}$| and |$K_{im-{\vee }}$| is provided by a class of frames that are based on Dunn’s compatibility frames. It is observed that this class coincides with one of the four classes giving the relational semantics for ILM and |${\textrm {ILM}}$|-|${\vee }$|⁠. (shrink)

Posner [6] has shown, by a nonuniform proof, that every ▵ 0 2 degree has a complement below 0'. We show that a 1-generic complement for each ▵ 0 2 set of degree between 0 and 0' can be found uniformly. Moreover, the methods just as easily can be used to produce a complement whose jump has the degree of any real recursively enumerable in and above $\varnothing'$ . In the second half of the paper, we show that the complementation (...) of the degrees below 0' does not extend to all recursively enumerable degrees. Namely, there is a pair of recursively enumerable degrees a above b such that no degree strictly below a joins b above a. (This result is independently due to S. B. Cooper.) We end with some open problems. (shrink)

Through contact algebras we study theories of mereotopology in a uniform way that clearly separates mereological from topological concepts. We identify and axiomatize an important subclass of closure mereotopologies called unique closure mereotopologies whose models always have orthocomplemented contact algebras , an algebraic counterpart. The notion of MT-representability, a weak form of spatial representability but stronger than topological representability, suffices to prove that spatially representable complete OCAs are pseudocomplemented and satisfy the Stone identity. Within the resulting class of contact algebras (...) the strength of the algebraic complementation delineates two classes of mereotopology according to the key ontological choice between mereological and topological closure operations. All closure operations are defined mereologically if and only if the corresponding contact algebras are uniquely complemented while topological closure operations highly restrict the contact relation but allow not uniquely complemented and nondistributive contact algebras. Each class contains a single ontologically coherent theory that admits discrete models. (shrink)

In this paper, I argue that not only PPs and adverbs can act as predicates of the event argument of the verb, but certain NPs and certain clauses can, as well. I will give syntactic and semantic arguments that NPs that are cognate objects and clauses of (at least some) nonbridge verbs are optional predicates of the event argument of the verb. With respect to clauses, I will argue that for independent reasons the meaning of both independent and embedded sentences (...) can be construed as event-properties, namely as properties of intentional events. (shrink)

A complement clause is used instead of a noun phrase; for example one can say either I heard [the result] or I heard [that England beat France]. Languages differ in the grammatical properties of complement clauses, and the types of verbs which take them. Some languages lack a complement clause construction but instead employ other construction types to achieve similar ends; these are called complementation strategies. The book explores the variety of types of complementation found across the languages of the (...) world, their grammatical properties and meanings. Detailed studies of particular languages, including Akkadian, Israeli, Jarawara, and Pennsylvania German, are framed by R. M. W. Dixon's introduction, which sets out the range of issues, and his conclusion, which draws together the evidence and the arguments. This book will interest scholars of typology, language universals, syntax, information structure, and language contact in departments of linguistics and anthropology, as well as advanced and graduate students taking courses in these subjects. (shrink)